A STUDY OF FUZZY COMPATIBILITY RELATIONS AND THEIRAPPLICATIONS
A STUDY OF FUZZY COMPATIBILITY RELATIONS AND THEIRAPPLICATIONS
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Date
2016-05
Authors
YASHIM, JAGABA MATHIAS
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Abstract
In this dissertation, various concepts for comparing fuzzy objects such as similarity, dissimilarity, symmetric similarity, relative similarity, multi-dimensional, and multi-attributes were studied. Some existing models such as Jaccard, Simple Matching Co-efficient, Vector, and Tversky were closely studied. The similarity measures introduced by Tversky(1977) and modified by (Dubois and Prade, 1980) using the cardinality of fuzzy sets and scalar evaluators and their operations such as T-norms (𝑇1,𝑇2,𝑇3) and T-conorms(𝑆1,𝑆2,𝑆3) were systematized. Finally,a new approach (Set Theoretic Measures) for comparing fuzzy objects by taking into consideration the degree of inclusion, partial matching and similarity was presented, some properties of the modified model elaborated and some areas of applications were identified.
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A DISSERTATION SUBMITTED TO THE SCHOOL OF POSTGRADUATE STUDIES, AHMADU BELLO UNIVERSITY, ZARIA, IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE AWARD OF MASTER OF SCIENCE IN MATHEMATICS
DEPARTMENT OF MATHEMATICS
FACULTY OF SCIENCE
AHMADU BELLO UNIVERSITY, ZARIA
NIGERIA
Keywords
STUDY,, FUZZY COMPATIBILITY RELATIONS,, APPLICATIONS,